LMIs in Control/pages/Stability of Lure systems

The SystemEdit


The DataEdit

The matrices  .

The LMI: The Lure's System's StabilityEdit

The following feasibility problem should be solved as sufficient condition for the stability of the above Lur'e system.





If the feasibility problem with LMI constraints has solution, then the Lure's system is stable.


The LMI is only a sufficient condition for the existence of a Lur’e Lyapunov function that proves stability of Lur'e system . It is also necessary when there is only one nonlinearity, i.e., when  .

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